DOI QR코드

DOI QR Code

A fast precise integration method for structural dynamics problems

  • Gao, Q. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology) ;
  • Wu, F. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology) ;
  • Zhang, H.W. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology) ;
  • Zhong, W.X. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology) ;
  • Howson, W.P. (Cardiff School of Engineering, Cardiff University) ;
  • Williams, F.W. (Cardiff School of Engineering, Cardiff University)
  • 투고 : 2011.09.18
  • 심사 : 2012.05.16
  • 발행 : 2012.07.10

초록

A fast precise integration method (FPIM) is proposed for solving structural dynamics problems. It is based on the original precise integration method (PIM) that utilizes the sparse nature of the system matrices and especially the physical features found in structural dynamics problems. A physical interpretation of the matrix exponential is given, which leads to an efficient algorithm for both its evaluation and subsequently the solution of large-scale structural dynamics problems. The proposed algorithm is accurate, efficient and requires less computer storage than previous techniques.

키워드

참고문헌

  1. Bathe, K.J. and Wilson, E.L. (1976), Numerical Methods in Finite Element Analysis, Prentice-Hall, New Jersey.
  2. Cai, Z.Q., Gu, Y.X. and Zhong, W.X. (2001), "A new approach of computing Floquet transition matrix", Comput. Struct., 79(6), 631-635. https://doi.org/10.1016/S0045-7949(00)00169-3
  3. Chen, B.S., Gu, Y.X., Guan, Z.Q. and Zhang, H.W. (2001), "Nonlinear transient heat conduction analysis with precise time integration method", Numer. Heat Tr. B-Fund., 40(4), 325-341. https://doi.org/10.1080/104077901317091712
  4. Fu, M.H., Cheung, M.C. and Sheshenin, S.V. (2010), "Precise integration method for solving singular perturbation problems", Appl. Math. Mech., 31(11), 1463-1472. https://doi.org/10.1007/s10483-010-1376-x
  5. Fung, T.C. (1997), "A precise time-step integration method by step-response and impulsive-response matrices for dynamic problems", Int. J. Numer. Meth. Eng., 40(24), 4501-4527. https://doi.org/10.1002/(SICI)1097-0207(19971230)40:24<4501::AID-NME266>3.0.CO;2-U
  6. Fung, T.C. and Chen, Z.L. (2006), "Krylov precise time-step integration method", Int. J. Numer. Meth. Eng., 68(11), 1115-1136. https://doi.org/10.1002/nme.1737
  7. Gu, Y.X., Chen, B.S., Zhang, H.W. and Guan, Z.Q. (2001), "Precise time-integration method with dimensional expanding for structural dynamic equations", AIAA J., 39(12), 2394-2399. https://doi.org/10.2514/2.1248
  8. Hairer, E., Lubich, C. and Wanner, G. (2006), Geometric Numerical Integration: Structure-preserving Algorithm for Ordinary Differential Equations, 2nd Edition, Springer, New York.
  9. Hairer, E., Norsett, S.P. and Wanner, G. (1993), Solving Ordinary Differential Equations I-nonstiff Problems, 2nd Edition, Springer, Berlin.
  10. Hairer, E. and Wanner, G. (1996), Solving Ordinary Differential Equations II-stiff and Differential- Algebraic Problems, 2nd Edition, Springer, Berlin.
  11. Jia, L., Shi, W. and Guo, J. (2008), "Arbitrary-difference precise-integration method for the computation of electromagnetic transients in single-phase nonuniform transmission line", IEEE Trans. Power Del., 23(3), 1488-1494.
  12. Leung, A.Y.T. (2001), "Fast matrix exponent for deterministic or random excitations", Int. J. Numer. Meth. Eng., 50(2), 377-394. https://doi.org/10.1002/1097-0207(20010120)50:2<377::AID-NME29>3.0.CO;2-E
  13. Lin, J.H., Shen, W.P. and Williams, F.W. (1995), "A high precision direct integration scheme for structures subjected to transient dynamic loading", Comput. Struct., 56(1), 113-120. https://doi.org/10.1016/0045-7949(94)00537-D
  14. Lin, J.H., Shen, W.P. and Williams, F.W. (1997), "Accurate high-speed computation of non-stationary random structural response", Eng. Struct., 19(7), 586-593. https://doi.org/10.1016/S0141-0296(97)83154-9
  15. Lin, J.H., Shen, W.P. and Williams, F.W. (1997), "Accurate high-speed computation of non-stationary random structural response", Eng. Struct., 19(7), 586-593. https://doi.org/10.1016/S0141-0296(97)83154-9
  16. Moler, C. and Loan, C.V. (1978), "Nineteen dubious ways to compute the exponential of a matrix", SIAM Rev., 20(4), 801-836. https://doi.org/10.1137/1020098
  17. Moler, C. and Loan, C.V. (2003), "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later", SIAM Rev., 45(1), 1-46. https://doi.org/10.1137/SIREAD000045000001000001000001
  18. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech.-ASCE, 85(3), 67-94.
  19. Shen, W.P., Lin, J.H. and Williams, F.W. (1995), "Parallel computing for the high precision direct integration method", Comput. Meth. Appl. M., 126(3-4), 315-331. https://doi.org/10.1016/0045-7825(95)00824-K
  20. Wang, M.F. and Au, F.T.K. (2007), "Precise integration method without inverse matrix calculation for structural dynamic equations", Earthq. Eng. Vib., 6(1), 57-64. https://doi.org/10.1007/s11803-007-0661-2
  21. Wang, M.F. and Au, F.T.K. (2006), "Assessment and improvement of precise time step integration method", Comput. Struct., 84(12), 779-786. https://doi.org/10.1016/j.compstruc.2006.02.001
  22. Wang, M.F. and Au F.T.K. (2009), "Precise integration methods based on Lagrange piecewise interpolation polynomials", Int. J. Numer. Meth. Eng., 77(7), 998-1014. https://doi.org/10.1002/nme.2444
  23. Wang, M.F. (2011), "Reduced-order precise integration methods for structural dynamic equations", Int. J. Numer. Meth. Biomed. Eng., 27(10), 1569-1582. https://doi.org/10.1002/cnm.1382
  24. Zhang, H.W., Chen, B.S. and Gu, Y.X. (2001), "An adaptive algorithm of precise integration for transient analysis", ACTA Mech. Solida Sin., 14(3), 215-224.
  25. Zhang, H.W., Zhang, X.W. and Chen, J.S. (2003), "A new algorithm for numerical solution of dynamic elastic- plastic hardening and softening problems", Comput. Struct., 81(17), 1739-1749. https://doi.org/10.1016/S0045-7949(03)00167-6
  26. Zhong, W.X. (2004), "On precise integration method", J. Comput. Appl. Math., 163(1), 59-78. https://doi.org/10.1016/j.cam.2003.08.053
  27. Zhong, W.X. and Williams, F.W. (1994), "A precise time step integration method", P. I. Mech. Eng. C-J. Mec., 208(6), 427-430. https://doi.org/10.1243/PIME_PROC_1994_208_148_02
  28. Zhong, W.X., Zhu, J. and Zhong, X.X. (1996), "On a new time integration method for solving time dependent partial differential equations", Comput. Meth. Appl. M., 130(1-2), 163-178. https://doi.org/10.1016/0045-7825(95)00876-4

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